Assignment Problems

Section 9.1

  1. True or False? A correlation coefficient, r=−0.8, represents a linear correlation that is less strong than when r=0.8.
  2. Using the scatter plot in Figure 1, state whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables.
Figure 1. Scatter plot: What type of correlation is shown?
Figure 1, What type of correlation is shown?

Problems 3-5 Use the data sets in Table 1 to answer the questions.

Table 1. The number of crimes reported (in millions) and the number of arrests reported (in millions) by the U.S. Department of Justice for 14 years.
Crimes, x 1.60 1.55 1.44 1.40 1.32 1.23 1.22
Arrests,y 0.78 0.80 0.73 0.72 0.68 0.64 0.63
Crimes, x 1.23 1.22 1.18 1.16 1.19 1.21 1.20
Arrests,y 0.63 0.62 0.60 0.59 0.60 0.61 0.58
  1. Display the data in a scatter plot. (Please, orient the x and y-axes in the usual way.)
  2. Calculate the correlation coefficient, r (Note: use technology for the calculation).
  3. What do you conclude about the type of correlation?

Section 9.2

  1. When are predictions made using a regression line meaningful?
  2. If the correlation between x and y is not significant, what is the best value to use when predicting y?

Problems 8-11. Use the data in Table 2 to answer the questions.

Table 2.
x 37 39 43 45 41 47
y 76 82 77 59 91 56
  1. What is the equation of the regression line?
  2. Construct a scatter plot for the data showing the regression line and the data points on the same graph.

Problems 10-11. Use the regression equation found in question 9 to predict the value of y for the values of x given. If it is not meaningful to predict the value of y, explain why not.

  1. x=40
  2. x=25

Section 3.1

Problems 12-13. Answer the following questions. A probability experiment is conducted by first spinning the spinner shown in Figure 2, then tossing a coin.

Figure 2. Spinner
Figure 2: A spinner used in the probability experiment.
  1. What set represents the sample space (Note: show all elements of the sample space using set notation.)
  2. Draw a tree diagram for the probability experiment.
  3. Multiple Choice Quiz. A multiple choice quiz has five possible answers per question. Assuming that no questions are left unanswered, in how many ways can an 8 question multiple choice quiz be answered?
  4. True or False? A probability of 0.08 is considered unusual.
  5. True or False? A probability always lies in the interval [0,1] on the real number line.
  6. Probability Experiment. A probability experiment consists of spinning the spinner (Note: The spinner is the same one specified for problems 12 and 13.) and rolling a six-sided die. What is the probability of spinning an even number and then rolling an odd number greater than 2? (Note: you can assume an equal probability for all numbers on the spinner and the die toss.)
  7. Use the frequency distribution in Table 3. Find the probability that a voter chosen at random is between 35 and 64 years old?.
Table 3. Ages of Voters
Ages of Voters Frequency
(in millions)
18 to 20 years old 6.4
21 to 24 years old 7.6
25 to 34 years old 22.3
35 to 44 years old 29.4
45 to 64 years old 57.2
65 years old and over 28.5
  1. Use the pie chart in Figure 3 to find the probability that a student attained less than B on the quiz?
Figure 3. The grades attained by students on a recent quiz.
Figure 3: A pie chart representing the grades attained by students on a recent quiz.

Section 3.2

  1. Classifying Events. A ball numbered 1 though 52 is selected from a bin, replaced, and then a second ball is selected from the bin. Are the events independent or dependent?

Problems 21-25.Use the information in Table 4 to answer the questions.

Table 4. Students Enrolled in Nursing
Males 203 1305 1508
Females 841 1498 2339
Total 1044 2803 3847
  1. Find the probability that a randomly selected student is a nursing major.
  2. Find the probability that a randomly selected student is female.
  3. Find the probability that a randomly selected student is a nursing major given that the student is a female.
  4. Find the probability that a randomly selected student is a nursing major and male.
  5. Are the events being a male student and being a nursing major independent or dependent events? Show the probability calculations that support your answer.